INSTRUCTIONS
1. DO NOT OPEN THIS BOOKLET UNTIL YOUR PROCTOR TELLS
YOU.
2. This is a twenty-five question multiple choice test. Each question is followed
by answers marked A, B, C, D and E. Only one of these is correct.
3. The answers to the problems are to be marked on the AMC 8 Answer Form
with a #2 pencil. Check the blackened circles for accuracy and erase errors
and stray marks completely. Only answers properly marked on the answer
form will be graded.
4. There is no penalty for guessing. Your score on this test is the number of
correct answers.
5. No aids are permitted other than scratch paper, graph paper, rulers, erasers,
and calculators that are accepted for use on the SAT. No problems on the test
will require the use of a calculator.
6. Figures are not necessarily drawn to scale.
7. Before beginning the test, your proctor will ask you to record certain informa-
tion on the answer form.
8. When your proctor gives the signal, begin working on the problems. You will
have 40 minutes to complete the test.
9. When you finish the exam, sign your name in the space provided on the
Answer Form.
The Committee on the American Mathematics Competitions reserves the right to re-examine students before
deciding whether to grant official status to their scores. The Committee also reserves the right to disqualify all
scores from a school if it is determined that the required security procedures were not followed.
The publication, reproduction, or communication of the problems or solutions of the AMC 8 during the period
when students are eligible to participate seriously jeopardizes the integrity of the results. Duplication at any time
via copier, telephone, e-mail, World Wide Web or media of any type is a violation of the copyright law.
Copyright © 2002, Committee on the American Mathematics Competitions,
Mathematical Association of America
The MaTheMaTical associaTion of aMerica
American Mathematics Competitions
PresenTed by The akaMai foundaTion
18th Annual
AMC 8
(American Mathematics Contest 8)
Tuesday, NOVEMBER 19, 2002
18th AMC 8 2002 2
1. A circle and two distinct lines are drawn on a sheet of paper. What is
the largest possible number of points of intersection of these figures?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
2. How many different combinations of $5 bills and $2
bills can be used to make a total of $17? Order does
not matter in this problem.
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
3. What is the smallest possible average of four distinct positive even
integers?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
4. The year 2002 is a palindrome (a number that reads the same from
left to right as it does from right to left). What is the product of the
digits of the next year after 2002 that is a palindrome?
(A) 0 (B) 4 (C) 9 (D) 16 (E) 25
5. Carlos Montado was born on Saturday, November 9, 2002. On what
day of the week will Carlos be 706 days old?
(A) Monday (B) Wednesday (C) Friday (D) Saturday (E) Sunday
6. A birdbath is designed to overflow so that it will
be self-cleaning. Water flows in at the rate of 20
milliliters per minute and drains at the rate of 18
milliliters per minute. One of these graphs shows the
volume of water in the birdbath during the filling time and continuing
into the overflow time. Which one is it?
A B C D E
Time
V
o
l
u
m
e
Time
V
o
l
u
m
e
Time
V
o
l
u
m
e
Time
V
o
l
u
m
e
Time
V
o
l
u
m
e
(A) A (B) B (C) C (D) D (E) E
18th AMC 8 2002 3
7. The students in Mrs. Sawyer’s class were asked to do a taste test of
five kinds of candy. Each student chose one kind of candy. A bar
graph of their preferences is shown. What percent of her class chose
candy E?
N
um
be
r
of
S
tu
de
nt
s
8
7
6
5
4
3
2
1
0
A B C D E
S W E E T T O O T H
Kinds of candy
(A) 5 (B) 12 (C) 15 (D) 16 (E) 20
Problems 8,9 and 10 use the data found in the accompanying paragraph
and table:
Juan’s Old Stamping Grounds
Juan organizes the stamps in his
collection by country and by the
decade in which they were issued.
The prices he paid for them at
a stamp shop were: Brazil and
France, 6c| each, Peru 4c| each, and
Spain 5c| each. (Brazil and Peru
are South American countries and
France and Spain are in Europe.)
Number of Stamps by Decade
Country ‘50s ‘60s ‘70s ‘80s
Brazil 4 7 12 8
France 8 4 12 15
Peru 6 4 6 10
Spain 3 9 13 9
Juan’s Stamp Collection
8. How many of his European stamps were issued in the ‘80s?
(A) 9 (B) 15 (C) 18 (D) 24 (E) 42
9. His South American stamps issued before the ‘70s cost him
(A) $0.40 (B) $1.06 (C) $1.80 (D) $2.38 (E) $2.64
10. The average price of his ‘70s stamps is closest to
(A) 3.5c| (B) 4c| (C) 4.5c| (D) 5c| (E) 5.5c|
18th AMC 8 2002 4
11. A sequence of squares is made of identical
square tiles. The edge of each square is one
tile length longer than the edge of the previous
square. The first three squares are shown. How many more tiles does
the seventh square require than the sixth?
(A) 11 (B) 12 (C) 13 (D) 14 (E) 15
B
A
C
12. A board game spinner is divided into three regions
labeled A, B and C. The probability of the arrow
stopping on region A is 13 and on region B is
1
2 . The
probability of the arrow stopping on region C is
(A) 112 (B)
1
6 (C)
1
5 (D)
1
3 (E)
2
5
13. For his birthday, Bert gets a box that holds 125
jellybeans when filled to capacity. A few weeks
later, Carrie gets a larger box full of jellybeans. Her
box is twice as high, twice as wide and twice as long as Bert’s.
Approximately, how many jellybeans did Carrie get?
(A) 250 (B) 500 (C) 625 (D) 750 (E) 1000
14. A merchant offers a large group of items at 30% off. Later, the mer-
chant takes 20% off these sale prices and claims that the final price of
these items is 50% off the original price. The total discount is
(A) 35% (B) 44% (C) 50% (D) 56% (E) 60%
15. Which of the following polygons has the largest area?
� � � � �
(A) A (B) B (C) C (D) D (E) E
18th AMC 8 2002 5
16. Right isosceles triangles are constructed on the sides of a 3-4-5 right
triangle, as shown. A capital letter represents the area of each triangle.
Which one of the following is true?
Z
W
X
Y
5
4
3
(A) X + Z =W + Y (B) W +X = Z (C) 3X + 4Y = 5Z
(D) X +W = 12(Y + Z) (E) X + Y = Z
17. In a mathematics contest with ten problems, a student gains 5 points
for a correct answer and loses 2 points for an incorrect answer. If
Olivia answered every problem and her score was 29, how many correct
answers did she have?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
18. Gage skated 1 hr 15 min each day for 5 days and 1 hr 30 min each day
for 3 days. How long would he have to skate the ninth day in order to
average 85 minutes of skating each day for the entire time?
(A) 1 hr (B) 1 hr 10 min (C) 1 hr 20 min (D) 1 hr 40 min (E) 2 hr
19. How many whole numbers between 99 and 999 contain exactly one 0?
(A) 72 (B) 90 (C) 144 (D) 162 (E) 180
20. The area of triangle XY Z is 8 square inches. Points A and B are
midpoints of congruent segments XY and XZ. Altitude XC bisects
Y Z. The area (in square inches) of the shaded region is
X
Y Z
A B
C
(A) 112 (B) 2 (C) 2
1
2 (D) 3 (E) 3
1
2
18th AMC 8 2002 6
21. Harold tosses a nickel four times. The probability that
he gets at least as many heads as tails is
(A) 516 (B)
3
8 (C)
1
2 (D)
5
8 (E)
11
16
22. Six cubes, each an inch on an edge, are fastened
together, as shown. Find the total surface area in
square inches. Include the top, bottom and sides.
(A) 18 (B) 24 (C) 26 (D) 30 (E) 36
23. A corner of a tiled floor is shown. If the
entire floor is tiled in this way and each of
the four corners looks like this one, then
what fraction of the tiled floor is made of
darker tiles?
(A) 13 (B)
4
9 (C)
1
2 (D)
5
9 (E)
5
8
24. Miki has a dozen oranges of the same size and
a dozen pears of the same size. Miki uses her
juicer to extract 8 ounces of pear juice from
3 pears and 8 ounces of orange juice from 2
oranges. She makes a pear-orange juice blend
from an equal number of pears and oranges. What percent of the blend
is pear juice?
(A) 30 (B) 40 (C) 50 (D) 60 (E) 70
25. Loki, Moe, Nick and Ott are good friends. Ott had no money, but
the others did. Moe gave Ott one-fifth of his money, Loki gave Ott
one-fourth of his money and Nick gave Ott one-third of his money.
Each gave Ott the same amount of money. What fractional part of
the group’s money does Ott now have?
(A) 110 (B)
1
4 (C)
1
3 (D)
2
5 (E)
1
2
SOLUTIONS
Your School Manager will be sent at least one copy of the 2002 AMC 8 Solutions Pam-
phlet. It is meant to be loaned to students (but not duplicated).
WRITE TO US
Comments about the problems and solutions for this AMC 8 should be addressed to:
Ms. Bonnie Leitch, AMC 8 Chair / bleitch@tenet.edu
548 Hill Avenue, New Braunfels, TX 78130
Comments about administrative arrangements should be addressed to:
Titu Andreescu, MAA AMC Director / tandreescu@unl.edu
American Mathematics Competitions, University of Nebraska-Lincoln
P.O. Box 81606, Lincoln, NE 68501-1606
AMC 10 & AMC 12
The AMC 10 and AMC 12 are 25-question, 75-minute contests with 5 choices of answers
for each problem (A through E). Schools with high scoring students on the AMC 8 will
receive an Invitation Brochure for the 2003 AMC 10. The best way to prepare for these
upper level contests is to study exams from previous years. Orders for all publications
listed below should be addressed to:
American Mathematics Competitions
ATTN: Publications
P.O. Box 81606
Lincoln, NE 68501-1606
PUBLICATIONS
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Make checks payable to the American Mathematics Competitions; or give your Visa, Mas-
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International Orders: Do NOT prepay; an invoice will be sent to you.
Each price is for an exam and its solutions for one year. Specify the years you want and
how many copies of each exam. All prices effective to September 1, 2003.
AMC 8 (Junior High/Middle School exam), 1990-2002, $1.00 per copy per year.
AMC 10 & AMC 12 (High School Exam), 1990-2002, $1.00 per copy per year.
Books (Exams and Solutions)
Problem Book I, AHSMEs 1950-1960, ............................$10.00
Problem Book II, AHSMEs 1961-1965, .......................... $10.00
Problem Book III, AHSMEs 1966-1972, .........................$13.00
Problem Book IV, AHSMEs 1973-1982, .........................$13.00
Problem Book V, AHSMEs & AIMEs 1983-1988, ..........$30.00
Problem Book VI, AHSMEs 1989-1994 ...........................$18.00
2002 AMC 8
DO NOT OPEN UNTIL
TUESDAY, NOVEMBER 19, 2002
**Administration On An Earlier Date Will Disqualify Your School’s Results**
1. All information (Rules and Instructions) needed to administer this exam is
contained in the TEACHERS’ MANUAL, which is outside of this package.
PLEASE READ THE MANUAL BEFORE NOVEMBER 19, 2002. Noth-
ing is needed from inside this package until November 19.
2. Your PRINCIPAL or VICE-PRINCIPAL must verify on the AMC 8 CER-
TIFICATION Form that all rules associated with the conduct of the exam
were followed.
3. The Answer Forms must be mailed First Class to the AMC office no later
than 24 hours following the exam.
4. THE AMC 8 IS TO BE ADMINISTERED DURING A CONVENIENT
40 MINUTE PERIOD. THE EXAM MAY BE GIVEN DURING A
REGULAR MATH CLASS.
5. The publication, reproduction or communication of the problems or solutions of this
test during the period when students are eligible to participate seriously jeopardizes
the integrity of the results. Duplication at any time via copier, telephone, e-mail,
World Wide Web or media of any type is a violation of the copyright law.
Major Sponsors
The Mathematical Association of America
The Akamai Foundation
University of Nebraska - Lincoln
Contributors
American Statistical Association Casualty Actuarial Society
Society of Actuaries National Council of Teachers of Mathematics
American Society of Pension Actuaries American Mathematical Society
American Mathematical Association of Two Year Colleges Pi Mu Epsilon
Consortium for Mathematics and its Applications Mu Alpha Theta
National Association of Mathematicians Kappa Mu Epsilon
School Science and Mathematics Association Clay Mathematics Institute
Institute for Operations Research and the Management Sciences
Canada/USA Mathcamp and Mathpath